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Results tagged with sobolev-spaces
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user 103725
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
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What is the optimal constant for the injection of $H^1$ into $L^\infty$ on an interval?
Let $I\subset \mathbb R$ be an interval, $1\leq p\leq \infty$, and $W^{1,p}(I)$ the usual Sobolev space. It is known that the injection $W^{1,p}(I)\hookrightarrow L^\infty(I)$ holds, i.e. there exists …
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